CN101719268A

CN101719268A - Generalized Gaussian model graph denoising method based on improved Directionlet region

Info

Publication number: CN101719268A
Application number: CN200910219348A
Authority: CN
Inventors: 焦李成; 侯彪; 张冬翠; 刘芳; 王爽; 张向荣; 马文萍
Original assignee: Xidian University
Current assignee: Xidian University
Priority date: 2009-12-04
Filing date: 2009-12-04
Publication date: 2010-06-02
Anticipated expiration: 2029-12-04
Also published as: CN101719268B

Abstract

The invention discloses a generalized Gaussian model graph denoising method based on an improved Directionlet region, which mainly solves the problems of serious loss of edge details and excessive smooth uniform region of the traditional denoising method. The generalized Gaussian model graph denoising method is realized by the following steps of: (1), selecting a test graph, and adding Gaussian noise to obtain a noise graph; (2), carrying out subgraph segmentation on the noise graph, determining a transformation matrix of each subgraph; (3), sampling the subgraphs to obtain cosets; (4), carrying out anisotropic wavelet transform on the cosets; (5), estimating shape parameters and local standard deviations of a high-frequency sub-band generalized Gaussian model; (6), estimating noise-free coefficients by using noise-containing coefficients; (7), carrying out anisotropic wavelet inverse transform on the noise-free coefficients; (8), weighting and synthesizing according to the transformation matrixes, reconstructing the subgraphs; and (9), synthesizing the reconstructed subgraphs to obtain the denoising result. The invention has the advantages of good edge details maintenance, little uniform region loss and high peak signal-to-noise, and can be used for removing Gaussian noise in a natural graph.

Description

Generalized Gaussian model image denoising method based on improved Directionlet domain

Technical Field

The invention belongs to the technical field of digital image processing, in particular to an image denoising method which can be used for removing noise in polluted natural images.

Background

Images are often contaminated with noise during acquisition and transmission. How to denoise an image and retain as much detail information of the image as possible to improve the quality of the image becomes an important task in image processing. According to the characteristics of the image, the statistical characteristics of the noise and the distribution rule of the frequency spectrum, people develop various denoising methods, wherein the most intuitive method is to perform denoising by adopting low-pass filtering, such as sliding average window filtering, Wiener filtering and the like, according to the characteristic that the noise is generally concentrated in high frequency and the frequency spectrum of the image is distributed in a limited interval. Other denoising methods include a method based on rank-order filtering, a method based on a markov field model, and the like, which have only a local analysis performance in a spatial domain or a frequency domain.

In recent years, because wavelets have good time-frequency characteristics and multi-resolution characteristics, the wavelet threshold method is widely applied to various denoising processes, but when threshold denoising is performed on a high-frequency coefficient subjected to orthogonal wavelet transform, overkill occurs, and the edge of a denoised image generates an oscillation phenomenon. The smooth wavelet transform with unchanged translation is developed on the basis of the wavelet, so that the defects in denoising of orthogonal wavelet transform are overcome, but the phenomenon of over-smoothness occurs in a uniform region in threshold denoising. A multi-scale geometric tool Contourlet which is used for solving the singularity of two dimensions or higher is close to the optimal approximation of a singular curve in an image, edge information is less lost when a Contourlet threshold value is denoised, but false components can be generated in a uniform area, namely mosquito noise is obvious.

The Directionlet transform proposed by Vladan Velisavljevi' is a new multi-scale geometric analysis tool. When the direction of the Directionlet base function is matched with the direction of the anisotropic target in the image, the approximation effect on the image is good, and detail information such as the edge of the image can be expressed sparsely; the Directionlet degrades to a wavelet when there is no match. However, in the existing Directionlet transformation, the transformation direction and the queue direction are all selected at will, such as 0 degree, 90 degrees, 45 degrees and-45 degrees, and direction self-adaptive transformation is not performed according to the characteristics of an image, so that edge information is seriously lost when the image is denoised, and a fuzzy distortion phenomenon occurs.

Disclosure of Invention

The invention aims to overcome the defects of the prior art and provide a generalized Gaussian model image denoising method based on an improved Directionlet domain, so as to perform direction self-adaptive transformation according to the characteristics of an image, achieve the aim of keeping detailed characteristics such as image edges and the like as far as possible while removing noise, and improve the quality of the image.

The technical scheme for realizing the aim of the invention is that firstly, a transformation matrix of Directionlet transformation is determined in a self-adaptive manner, so that the transformation matrix is transformed according to the main direction of an image, a generalized Gaussian model is used for modeling a Directionlet coefficient during denoising, different noise-free coefficient estimation strategies are adopted according to the size of the shape parameter of the generalized Gaussian model and the local standard deviation, and the image is denoised, wherein the specific denoising steps comprise the following steps:

(1) selecting a test image, and adding zero-mean Gaussian noise to obtain a noise image;

(2) 64 x 64 subgraph segmentation is carried out on the noise image, and a Directionlet transformation matrix M of each segmented subgraph is adaptively determined by using binary wavelet transformation_Λ；

(3) Using transformation matrix M_ΛSampling each divided sub-graph to obtain | det (M) of the divided sub-graph_Λ) L cosets, | det (M)_Λ) Is the matrix M_ΛAbsolute value of determinant;

(4) transforming matrix M along Directionlet for each coset of each divided subgraph_ΛRespectively carry out n in the conversion direction and the queue direction of₁2 and n₂Obtaining high-frequency and low-frequency subband coefficients of Directionlet transform by 1-time one-dimensional wavelet transform;

(5) for each high-frequency sub-band, estimating the shape parameter upsilon and the local standard deviation sigma of the generalized Gaussian model by using all the transformation coefficients of the sub-band_x；

(6) Judging the shape parameter upsilon of the generalized Gaussian model of each high-frequency sub-band:

if the upsilon is more than 0 and less than 0.5, estimating the noise-free coefficient of the noise image according to the following formula,

<math><mrow><mover><mi>x</mi><mo>^</mo></mover><mrow><mo>(</mo><mi>y</mi><mo>)</mo></mrow><mo>=</mo><mfenced open='{' close=''><mtable><mtr><mtd><mn>0</mn><mo>,</mo></mtd><mtd><mo>|</mo><mi>y</mi><mo>|</mo><mo><</mo><msub><mi>T</mi><mi>&upsi;</mi></msub></mtd></mtr><mtr><mtd><mi>y</mi><mo>-</mo><msup><mi>σ</mi><mn>2</mn></msup><msup><msub><mi>σ</mi><mi>x</mi></msub><mrow><mo>-</mo><mi>&upsi;</mi></mrow></msup><mi>&upsi;η</mi><mrow><mo>(</mo><mi>&upsi;</mi><mo>)</mo></mrow><msup><mi>y</mi><mrow><mi>&upsi;</mi><mo>-</mo><mn>1</mn></mrow></msup><mo>+</mo><mi>o</mi><mrow><mo>(</mo><msup><mi>y</mi><mrow><mn>2</mn><mrow><mo>(</mo><mi>&upsi;</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow></mrow></msup><mo>)</mo></mrow><mo>,</mo></mtd><mtd><mo>|</mo><mi>y</mi><mo>|</mo><mo>&GreaterEqual;</mo><msub><mi>T</mi><mi>&upsi;</mi></msub></mtd></mtr></mtable></mfenced></mrow></math>

whereinIs an estimate of the noise-free coefficient, y is the noise-containing coefficient, T_υ＝C_υσ^2/(2-υ)σ_x ^-(υ/(2-υ))，C_υ＝(2-υ)(2-2υ)^-(1-υ/2-υ)η(υ)^υ/(2-υ)，

Γ is the function of Gamma and,

<math><mrow><mi>Γ</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>=</mo><msubsup><mo>&Integral;</mo><mn>0</mn><mo>∞</mo></msubsup><msup><mi>e</mi><mrow><mo>-</mo><mi>u</mi></mrow></msup><msup><mi>u</mi><mrow><mi>t</mi><mo>-</mo><mn>1</mn></mrow></msup><mi>du</mi><mo>,</mo></mrow></math>

o(y^2(υ-1)) Is y^2(υ-1)σ is the noise standard deviation, and Y ═ Y (Y)₁，y₂，...，y_N) Is the noisy high frequency subband coefficient, N is the number of high frequency subband coefficients;

if upsilon is more than or equal to 0.5 and less than 1, adopting a threshold value

Performing soft threshold processing;

(7) for low-frequency sub-band and estimated noiseless high-frequency sub-band edge matrix M_ΛRespectively carry out n in the conversion direction and the queue direction of₁2 and n₂1-time one-dimensional inverse wavelet transform;

(8) according to a transformation matrix M_ΛWeighted synthesis of transform direction and queue direction of (3), reconstructing each partitionA drawing;

(9) and synthesizing the reconstructed segmentation subgraphs according to the positions of the segmentation subgraphs in the original image to obtain a denoised image.

Compared with the prior art, the invention has the following advantages:

(1) the matrix adopting the Directionlet transformation is determined according to the characteristic self-adaption of the image, and because the Directionlet transformation coefficient is better approximated to the edge anisotropic characteristic in the image and better maintains the edge detail information when the image is denoised, the invention solves the problem that the existing Directionlet transformation method is degraded into wavelet transformation due to the random selection of the transformation matrix, and the edge blurring problem is caused by the inaccurate approximation to the edge anisotropic characteristic and the like and the serious loss of the edge information in the image denoising treatment;

(2) the invention fully considers the influence of the shape parameter of the generalized Gaussian model when estimating the noise-free coefficient, the adopted local standard deviation has local adaptability, and each coefficient of the high-frequency sub-band can be estimated more accurately, thereby solving the problems of 'over-killing' of the existing wavelet threshold method to the noise-containing coefficient and the problem of over-smoothing of the uniform region of the stationary wavelet threshold method.

Simulation experiment results show that in the process of denoising a natural image with Gaussian noise, the method has the advantages that the detail information such as edges and the like is well kept, the uniform area is clearer, the higher peak signal-to-noise ratio is obtained, and the quality of the image is improved.

Drawings

FIG. 1 is a schematic diagram of the principal operation of the present invention;

FIG. 2 is a comparison graph of the denoising effect of the test image Lena by using the method of the present invention and the existing denoising method;

FIG. 3 is a comparison graph of the denoising effect of the test image Barbara by the method of the present invention and the existing denoising method;

FIG. 4 is a comparison graph of the denoising effect of the test image Peppers by using the method of the present invention and the existing denoising method.

Detailed Description

Referring to fig. 1, the specific implementation steps of the present invention are as follows:

step 1: selecting a test image, adding Gaussian noise to obtain a noise image, wherein the mathematical expression of the noise image is as follows:

f＝g+n

wherein g ═ { g (i)₁，j₁)|i₁，j₁N denotes a test image, N ═ N (i) and 1, 2₁，j₁)|i₁，j₁N represents a mean value of zero variance σ²The noise image is expressed as f ═ f (i) as gaussian noise₁，j₁)|i₁，j₁N denotes an image size.

Step 2: dividing the noise image into 64 × 64 sub-images without overlapping, and finding two main directions θ of each sub-image₁And theta₂According to a main direction theta₁And theta₂Determining Directionlet transformation matrix M of each divided subgraph_ΛThe method comprises the following specific steps:

2a) performing dyadic wavelet transform on the segmentation subgraph to obtain a horizontal detail map h (i, j) and a vertical detail map v (i, j), wherein (i, j) is the position of a dyadic wavelet transform coefficient, and i, j is 1, 2.. 64;

2b) calculating the direction theta (i, j) of the segmentation subgraph at (i, j) according to h (i, j) and v (i, j):

if h (i, j) < v (i, j), i.e

| | \frac{| v (i, j) | - | h (i, j) |}{| v (i, j) |} | - 1 | < 0.05,

If h (i, j) > v (i, j), i.e

| | \frac{| v (i, j) | - | h (i, j) |}{| h (i, j) |} | - 1 | < 0.05,

θ(i，j)＝0；

If it is

Or

<math><mrow><mo>|</mo><mo>|</mo><mfrac><mrow><mo>|</mo><mi>v</mi><mrow><mo>(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo>)</mo></mrow><mo>|</mo><mo>-</mo><mo>|</mo><mi>h</mi><mrow><mo>(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo>)</mo></mrow><mo>|</mo></mrow><mrow><mo>|</mo><mi>h</mi><mrow><mo>(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo>)</mo></mrow><mo>|</mo></mrow></mfrac><mo>|</mo><mo>-</mo><mn>1</mn><mo>|</mo><mo>&GreaterEqual;</mo><mn>0.05</mn><mo>,</mo></mrow></math>

<math><mrow><mi>θ</mi><mrow><mo>(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo>)</mo></mrow><mo>=</mo><mi>arctan</mi><mfrac><mrow><mi>v</mi><mrow><mo>(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo>)</mo></mrow></mrow><mrow><mi>h</mi><mrow><mo>(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo>)</mo></mrow></mrow></mfrac><mo>;</mo></mrow></math>

2c) Counting the distribution of the directions theta (i, j) of the segmented subgraphs, and finding out the two directions theta (i, j) with the most occurrence times₁And theta₂；

2d) Separately solving two main directions theta₁And theta₂To obtain two approximate rational slopes r₁And r₂，r₁≈arctanθ₁＝b₁/a₁，r₂≈arctanθ₂＝b₂/a₂According to a rational slope r₁And r₂Constructing a transformation matrix

Wherein along r₁Is called a transformation matrix M_ΛIn the direction of r₂Is called the queue direction, a₁，a₂，b₁，b₂Are all integers.

And step 3: using transformation matrix M_ΛFor each of the divided subgraphs, the edge r is₁And r₂Sampling is carried out in the direction to obtain | det (M) of the segmentation subgraph_Λ) L cosets, | det (M)_Λ) Is the matrix M_ΛAbsolute value of determinant.

And 4, step 4: for each coset edge r of each segmented subgraph₁Direction of progress n₁2-fold one-dimensional wavelet transform along r₂Direction of progress n₂The high-frequency and low-frequency subband coefficients of the Directionlet transform are obtained by 1-time one-dimensional wavelet transform.

And 5: method for estimating shape parameter upsilon and local standard deviation sigma of generalized Gaussian model by noise-containing high-frequency subband coefficient_xThe method comprises the following steps:

3a) let the size of the high-frequency sub-band be l₁×l₂Calculating the second moment sigma of the high-frequency subband coefficient containing noise according to the formula_Y ²And kurtosis k of noisy high-frequency subband coefficients_Y：

σ_Y ⁴＝(σ_Y ²)²

In the formula

Is (i)₂，j₂) The square of the high frequency coefficient of the noise is measured,

is (i)₂，j₂) Processing the 4 th power of the high-frequency coefficient containing noise;

3b) and (3) solving the noise standard deviation by a median estimation method according to the noise-containing high-frequency sub-band coefficient Y:

<math><mrow><mi>σ</mi><mo>=</mo><mfrac><mrow><mi>Median</mi><mrow><mo>(</mo><mo>|</mo><mi>Y</mi><mo>|</mo><mo>)</mo></mrow></mrow><mn>0.6745</mn></mfrac><mo>,</mo></mrow></math>

and then, solving the standard deviation of the noise-free coefficient according to the noise standard deviation sigma:

3c) k obtained from the above_Y，σ_Y ²And sigma value, using a numerical calculation method to obtain a shape parameter upsilon according to the following formula:

3d) obtaining initial estimation value of noise-free coefficient by using minimum mean square error estimation method according to noise-containing high-frequency sub-band coefficient Y

Wherein,

is (i)₂，j₂) Of the noisy high-frequency coefficient of₂＝1，2，...l₁，j₂＝1，2，...l₂；

3e) From shape parametersAnd v and an initial estimation value X of a noise-free coefficient, and calculating a local standard deviation: sigma_x＝SE

Where S is a factor related only to the shape parameter v,

e is the absolute mean of the initial estimates of the noise-free coefficients in the local neighborhood of size 5 x 5,

is (i)₃+p，j₃+ q) initial estimate of the noise free coefficient,

i₃＝2，...l₁-1，j₃＝2，...l₂-1。

step 6: dividing a shape parameter upsilon into two intervals of more than upsilon and less than 0.5 and more than or equal to 0.5 and less than 1, and estimating a noise-free coefficient by using the following estimation strategy:

wherein

Is an estimate of the noise-free coefficient, y is the noise-containing coefficient, T_υ＝C_υσ^2/(2-υ)σ_x ^-(υ/(2-υ))，C_υ＝(2-υ)(2-2υ)^-(1-υ/2-υ)η(υ)^υ/(2-υ)，

Γ is the function of Gamma and,

o(y^2(υ-1)) Is y^2(υ-1)A high order infinitesimal quantity of (1), σ being the noise standard deviation;

And carrying out soft threshold processing on the noise-containing coefficient to obtain the estimation of the noise-free coefficient.

And 7: for the low-frequency sub-band and the estimated noise-free high-frequency sub-band edge r₁Direction of progress n₁2-fold inverse one-dimensional wavelet transform along r₂Direction of progress n₂1-time one-dimensional inverse wavelet transform.

And 8: for the result obtained in step 7 along r₁Direction sum r₂And carrying out weighted synthesis on the directions to reconstruct each segmentation subgraph.

And step 9: and synthesizing the reconstructed segmentation subgraphs according to the positions of the segmentation subgraphs in the original image to obtain a denoised image.

The effects of the present invention are further illustrated by the following simulations.

First, simulation condition

The method adopts standard images Lena 512 multiplied by 512, Barbara 512 multiplied by 512 and Peppers512 multiplied by 512 which are commonly used in image denoising, adds zero mean value additive Gaussian white noise with standard deviation sigma of 10, 15, 20, 25, 30, 35, 40, 45 and 50 to the three images respectively, and carries out simulation denoising processing by using the denoising method, the wavelet soft threshold denoising method, the stationary wavelet hard threshold denoising method, the Contourlet hard threshold denoising method and the Contourlet soft threshold denoising method respectively.

Second, simulation result analysis

Simulation 1, comparing the denoising effect of the method of the invention with that of the existing denoising method to the test image Lena, and the result is shown in fig. 2, wherein:

FIG. 2(a) is a test image Lena; fig. 2(b) is a Lena noisy image with σ ═ 20, peak signal-to-noise ratio PSNR ═ 22.13 dB; fig. 2(c) is a diagram of the denoising result of the wavelet soft threshold, PSNR is 26.74 dB; fig. 2(d) is a graph of the stationary wavelet hard threshold denoising result, with PSNR being 28.38 dB; FIG. 2(e) is a Contourlet hard threshold denoising result graph, with PSNR equal to 28.93 dB; fig. 2(f) is a graph of the noise removal result of Contourlet soft threshold, PSNR is 26.76 dB; FIG. 2(g) is a graph of the denoising result of the method of the present invention, where PSNR is 30.19 dB;

as can be seen from FIG. 2(a) and FIG. 2(c), after denoising by the conventional wavelet soft threshold method, oscillation occurs at the brim of Lena, and distortion of the face and other uniform regions is severe.

As can be seen from FIG. 2(d), although the brim of Lena is relatively clear after denoising by the conventional stationary wavelet hard threshold method, the texture on the hat is somewhat blurred, and the uniform region appears to be too smooth.

As can be seen from fig. 2(e) and 2(f), after denoising by the prior Contourlet threshold method, a false component is generated, i.e., mosquito noise is obvious.

As can be seen from FIG. 2(g), the texture on the brim and hat of the Lena after denoising by the method of the present invention is clearer, the face and other uniform regions are smoother, the distortion is less, and the peak signal-to-noise ratio is higher, so that the noise of FIG. 2(b) is effectively removed.

Simulation 2, comparing the denoising effect of the test image Barbara with that of the existing denoising method, and obtaining a result as shown in FIG. 3, wherein:

figure 3(a) is a test image, barbarara; fig. 3(b) is a Barbara noisy image with σ ═ 20, PSNR ═ 22.19 dB; fig. 3(c) is a diagram of the denoising result of the wavelet soft threshold method, where PSNR is 23.67 dB; fig. 3(d) is a graph of the denoising result of the stationary wavelet hard threshold method, where PSNR is 25.39 dB; FIG. 3(e) is a denoising result graph of Contourlet hard threshold method, where PSNR is 25.86 dB; fig. 3(f) is a denoising result graph of the Contourlet soft threshold method, where PSNR is 23.87 dB; FIG. 3(g) is a graph of the denoising result of the method of the present invention, where PSNR is 27.87 dB.

As can be seen from fig. 3(a) and 3(c), the texture information on Barbara trousers and scarf is seriously lost after denoising by the existing wavelet soft threshold method.

As can be seen from fig. 5(d), after denoising by the conventional stationary wavelet hard threshold method, the texture information on the Barbara trousers and scarf is lost, and the leg part of the table vibrates.

As can be seen from fig. 3(e) and 3(f), after denoising by the conventional Contourlet threshold denoising method, the Barbara texture remains good, the image is clearer, but a serious false component is generated, that is, mosquito noise is obvious.

As can be seen from fig. 3(g), the method of the present invention removes the noise from fig. 3(b) while maintaining more details of the texture at barbarbara pants, scarves, etc., and it can be seen that the present invention has considerable advantages in detail maintenance, and the uniform area is also clearer.

Simulation 3, comparing the denoising effect of the test image Peppers by using the method of the invention with the existing denoising method, and obtaining a result as shown in FIG. 4, wherein:

FIG. 4(a) is a test image Peppers; fig. 4(b) is a Peppers noisy image with σ ═ 20, PSNR ═ 22.21 dB; fig. 4(c) is a denoising result graph of the wavelet soft threshold method, where PSNR is 27.21 dB; fig. 4(d) is a graph of the denoising result of the stationary wavelet hard threshold method, where PSNR is 28.59 dB; FIG. 4(e) is a graph of the denoising result of Contourlet hard threshold method, with PSNR being 28.65 dB; fig. 4(f) is a denoising result graph of the Contourlet soft threshold method, where PSNR is 26.51 dB; FIG. 4(g) is a graph of the denoising result of the method of the present invention, where PSNR is 30.82 dB.

As can be seen from FIG. 4(a) and FIG. 4(c), after denoising, oscillation occurs at edges of Peppers in the conventional wavelet soft threshold method.

As can be seen from FIG. 4(d), after denoising by the conventional stationary wavelet hard threshold method, an over-smoothing phenomenon occurs in a uniform region of Peppers.

As can be seen from FIG. 4(e) and FIG. 4(f), the existing Contourlet threshold denoising method denoises more thoroughly, but mosquito noise is obvious.

As can be seen from FIG. 4(g), the method of the present invention has clear edges and clear uniform regions of various vegetables after denoising in FIG. 4(b), and has a smaller difference compared with the test image FIG. 4(a), which is obviously better than the denoising effect of other methods.

In conclusion, the method disclosed by the invention has the advantages of good visual effect, higher peak signal-to-noise ratio and greater advantage in the aspect of edge preservation.

Claims

1. A generalized Gaussian model image denoising method based on an improved Directionlet domain comprises the following steps:

(3) Using transformation matrix M_ΛSampling each divided sub-graph to obtain | det (M) of the divided sub-graph_Λ) L number of cosets，|det(M_Λ) Is the matrix M_ΛAbsolute value of determinant;

wherein

Is an estimate of the noise free coefficient, y is the noisy coefficient,

C_υ＝(2-υ)(2-2υ)^-(1-υ/2-υ)η(υ)^υ/(2-υ)，

Γ is the function of Gamma and,

Performing soft threshold processing;

2. The denoising method of claim 1, wherein the step (2) of adaptively determining the Directionlet transform matrix M of each segmented subgraph by using the dyadic wavelet transform_ΛThe method comprises the following steps:

if h (i, j) < v (i, j), i.e

| | \frac{| v (i, j) | - | h (i, j) |}{| v (i, j) |} | - 1 | < 0.05,

If h (i, j) > v (i, j), i.e

| | \frac{| v (i, j) | - | h (i, j) |}{| v (i, j) |} | - 1 | < 0.05,

θ(i，j)＝0；

If it is

| | \frac{| v (i, j) | - | h (i, j) |}{| v (i, j) |} | - 1 | > 0.05

Or

<math><mrow><mo>|</mo><mo>|</mo><mfrac><mrow><mo>|</mo><mi>v</mi><mrow><mo>(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo>)</mo></mrow><mo>|</mo><mo>-</mo><mo>|</mo><mi>h</mi><mrow><mo>(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo>)</mo></mrow><mo>|</mo></mrow><mrow><mo>|</mo><mi>v</mi><mrow><mo>(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo>)</mo></mrow><mo>|</mo></mrow></mfrac><mo>|</mo><mo>-</mo><mn>1</mn><mo>|</mo><mo>&GreaterEqual;</mo><mn>0.05</mn><mo>,</mo></mrow></math>

2c) Counting theta values of the segmented subgraphs, and finding out two directions theta with the most occurrence times₁And theta₂；

2d) By theta₁And theta₂To obtain an approximate rational slope r₁And r₂，r₁≈arctanθ₁＝b₁/a₁，r₂≈arctanθ₂＝b₂/a₂According to a rational slope r₁And r₂Constructing a transformation matrix

3. The denoising method according to claim 1, wherein said estimating step (5) estimates a shape parameter v and a local standard deviation σ of the generalized Gaussian model_xThe method comprises the following steps:

3a) let the size of the high-frequency sub-band be l₁×l₂Calculating the second moment sigma of the high-frequency subband coefficient containing noise from the high-frequency subband coefficient Y containing noise_Y ²And kurtosis k of noisy high-frequency subband coefficients_Y：

In the formula

Is (i)₂，j₂) The square of the high frequency coefficient of the noise is measured,is (i)₂，j₂) Processing the 4 th power of the high-frequency coefficient containing noise;

3c) k obtained from the above_Y，σ_Y ²And a σ value, and a shape parameter v is obtained by a numerical calculation method:

3d) obtaining initial estimation of noise-free coefficient by using minimum mean square error estimation method from noise-containing high-frequency sub-band coefficient Y

Wherein

Is (i)₂，j₂) And (c) processing the initial estimate of the noise-free coefficient, wherein,

3e) Calculating a local standard deviation by using the shape parameter upsilon and an initial estimation value X of a noise-free coefficient: sigma_x＝SE

Wherein

S is a factor related only to the shape parameter v,

is (i)₃+p，j₃+ q) initial estimate of the noise free coefficient, i₃＝2，...l₁-1，j₃＝2，...l₂-1, E is the absolute mean of the initial estimates of the noise-free coefficients in the local neighborhood of size 5 x 5.